The usual discussions of geometrical optics often rely too heavily on ray diagrams to locate the image and study its properties. We will demonstrate that all of these insights can be obtained purely by algebra on the mirror equation. Developing these instincts will help us solve optics problems without having to use crude, hand drawn, and often inaccurate ray diagrams. Our main results are summarized in the table below.
We begin by recalling the mirror equation
(1) 
where 
and 
the distances of the object and image from the mirror, and the focal length 
, for a spherical mirror with …
and same refractive index 
are placed on a horizontal surface as shown in figure. Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same (
). If 
, and 
are the apparent depths of a point 
on the bottom of the three cylinders, respectively, the correct statement(s) is/are:
